Empirical studies show that job search behavior depends on the financial situation of the unemployed. Starting from this observation, we ask how unemployment insurance policy should take the individual financial situation into account. We use a quantitative model with a realistically calibrated unemployment insurance system, individual consumption-saving decision and moral hazard during job search to answer this question and find that the optimal policy provides unemployment benefits that increase with individual assets. By implicitly raising interest rates, asset-increasing benefits encourage self-insurance, which facilitates consumption smoothing during unemployment, but does not exacerbate moral hazard for job search. Asset-increasing benefits also have desirable properties from a dynamic perspective, because they emulate key features of the dynamics of constrained efficient allocations. The welfare gain from introducing asset-increasing benefits is substantial and amounts to 1.5 % of consumption when comparing steady states and 0.8 % of consumption when taking transition costs into account. More generous replacement rates or benefits targeted to asset-poor households, by contrast, have a negative effect on welfare.